Wavelets in Applied and Pure Mathematics\ Postgraduate Course in Applied Analysis

Wavelets in Applied and Pure Mathematics
Postgraduate Course in Applied Analysis

Vladimir V. Kisil

University of Leeds, School of Mathematics

Web page: http://maths.leeds.ac.uk/~kisilv/courses/wavelets.html

Description: The course gives an overview of wavelets (or coherent states) construction and its realisations in applied and pure mathematics. After a short introduction to wavelets based on the representation theory of groups we will consider:

The variety of applications is essentially grouped just around three groups: the Heisenberg group, SL2(R), and ax+b group.

This course is suitable for postgraduate students in both applied and pure mathematics.

For on-line reading lecture notes are available in PDF (recommended!) or HTML formats. See Technical notes on viewing online materials. To print lecture notes use PostScript.
Contents:

  1. What Are Wavelets and What Are They Good for?

  2. Groups and Homogeneous Spaces.

  3. Representation Theory.

  4. Wavelets on Groups and Square Integrable Representations.

  5. Wavelets on Homogeneous Spaces: the Segal-Bargmann Space.

  6. Wavelets in Banach Spaces and Functional Calculus

Pre-requisites: Basic real and complex analysis, rudimentary algebra.

References

[1]
Syed Twareque Ali, Jean-Pierre Antoine, and Jean-Pierre Gazeau. Coherent states, wavelets and their generalizations. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 2000.

[2]
Michael E. Taylor. Noncommutative Harmonic Analysis, volume 22 of Math. Surv. and Monographs. American Mathematical Society, Providence, R.I., 1986.
Tecnical Notes:


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On 22 May 2003, 14:49.